Solving systems…..

Elimination Method!Lesson 2.9(y do I have to get rid of x?)

‘In Common’ Ballad: http://youtu.be/Br7qn4yLf-I‘All I do is solve’ Rap: http://youtu.be/1qHTmxlaZWQ

Concept: Solving Systems of Equations

Essential Question:How can I manipulate equation(s) to solve a system of equations? (standards REI 5-6, 10-11)

Vocabulary:Elimination/Algebraically/Linear Combination Method

Example 1Solve the following system by elimination.

1.Write your equations so that the corresponding variables are aligned.

Notice 2x is above x and -3y is above 3y

2. Check to see if the same variable has the same coefficient.

The coefficients y differ only by a sign.

3. Multiply to make the coefficients the same value, but different signs. Our example has 3y and -3y so we can move on to step 4.

4. Use addition to eliminate one of the variables.

5. Solve for the variable .

3x = 0 x = 0

6. Continue solving the system to find the remaining variable.

Using an original equation, substitute the value you found for y.

-3y = -11 y =

Solution: (0, 3

7. Write the solution as a point.

1.Write your equations so that the corresponding variables are aligned.

Notice x is above

3x and 4y is above

2y

Example 2:

x + 4y = 03x + 2y = 20

2. Check to see if the same variable has the same coefficient.

Example 2:

The coefficients are different for x and y.

x + 4y = 03x + 2y = 20

3. Multiply to make the coefficients the same value, but different signs.

x + 4y = 03x + 2y = 20

How can we make the coefficients of x the same but with different signs?

-3(x + 4y = 0) 3x + 2y = 20

- 3x - 12y = 0 3x + 2y = 20

4. Use addition to eliminate one of the variables.

5. Solve for the variable .

- 3x - 12y = 0 + 3x + 2y = 20 -10y = 20

-10y = 20 y = -2

6. Continue solving the system to find the remaining variable.

Using an original equation, substitute the value you found for y.

x + 4y = 0x + 4(-2) = 0x – 8 = 0 x = 8

Solution: (8, -2)

7. Write the solution as a point.

Notice 2x is above

3x and 3y is above

4y

Example 3:

1.Write your equations so that the corresponding variables are aligned.

2x + 3y = 93x + 4y = 15

2. Check to see if the same variable has the same coefficient.

Example 3:

The coefficients for x and y are not the same.

2x + 3y = 93x + 4y = 15

3. Use multiplication or division to make one of the variables have the same coefficient but different signs. How can we

make the coefficients of x the same but with different signs?

2x + 3y = 93x + 4y = 15

3(2x + 3y = 9)-2(3x + 4y = 15) 6x + 9y = 27-6x – 8y = -30

4. Use addition to eliminate one of the variables.

5. Solve for the variable (we can skip this step because the variable is already solved).

y = -3

6x + 9y = 27-6x – 8y = -30 y = -3

6. Continue solving the system to find the remaining variable.

Using an original equation, substitute the value you found for y.

2x + 3y = 92x + 3(-3) = 92x – 9 = 9 2x = 18 x = 9

Solution: (9, 3)

7. Write the solution as a point.

You Try!

You Try!

2

You Try!

3

You Try Challenge!4.

$2.00 Summary….

Each word is worth 10 cents. Write a summary describing how to solve a system using the elimination method.